[orlp]

That's a GCC skill issue. You can do it in five branchless instructions for unsigned by splitting the unsigned up in two 32-bit halves, converting those to floats simply by inserting their values as mantissa into constants 2^52 and 2^(52 + 32). This conversion is exact.

Then to finish the conversion you subtract 2^52 and 2^(52 + 32) respectively from the halves and add them together.

    vmovq       xmm0, rdi
    vpunpckldq  xmm0, xmm0, xmmword ptr [rip + .CONST1]
    vsubpd      xmm0, xmm0, xmmword ptr [rip + .CONST2]
    vshufpd     xmm1, xmm0, xmm0, 1
    vaddsd      xmm0, xmm1, xmm0

Here CONST1 = [0x43300000, 0x45300000, 0, 0] and CONST2 = [0, 0x43300000, 0, 0x45300000].